Stochastic Deep Networks - KCL-BMEIS/Methods_JournalClub GitHub Wiki
Presented by Samuel
27th of June 2019
Stochastic Deep Networks
Gwendoline de Bie, Gabriel Peyré, Marco Cuturi (2018)
Machine learning is increasingly targeting areas where input data cannot be accurately described by a single vector, but can be modeled instead using the more flexible concept of random vectors, namely probability measures or more simply point clouds of varying cardinality. Using deep architectures on measures poses, however, many challenging issues. Indeed, deep architectures are originally designed to handle fixed length vectors, or, using recursive mechanisms, ordered sequences thereof. In sharp contrast, measures describe a varying number of weighted observations with no particular order. We propose in this work a deep framework designed to handle crucial aspects of measures, namely permutation invariances, variations in weights and cardinality. Architectures derived from this pipeline can (i) map measures to measures - using the concept of push-forward operators; (ii) bridge the gap between measures and Euclidean spaces - through integration steps. This allows todesign discriminative networks (to classify or reduce the dimensionality of input measures), generative architectures (to synthesize measures) and recurrent pipelines (to predict measure dynamics). We provide a theoretical analysis of these building blocks, review our architectures' approximation abilities and robustness w.r.t. perturbation, and try them on various discriminative and generative tasks.
Discussion Points
The paper considers probability distributions as input and output. What are the benefits/drawbacks of this paradigm?
- Considering the uncertainty of the samples can be useful when the knowledge about the sample itself is not good. On the other hand, we can derive the sample from other estimations (such as imputation).
- The method compresses the information to go from a point in a high dimensional space into a distribution lying in lower-dimensional space.
Drawback:
- Computationally expensive;
- The data is not in the correct form -> it needs to be re-designed, encoded etc...
Application to the medical imaging field
Methods
- Registration;
- Probabilistic ground truth for segmentation from clinicians;
- Parameterised 3D structures that can be translated into point clouds - Cardiac application based on a mesh created from the segmentation;
- Uncertain inputs due to measurements and/or imputed values.
Clinical data
- Cardiac mesh